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We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom of the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in view of softening the known discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.

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The paper deals with the problem of choosing the best O&M strategy for wind power plants. Current maintenance theory considers just production opportunities and minimizes the maintenance costs, but with the liberalization of the electricity market also the electricity price has become an important variable to take into account in the O&M scheduling. Another important variables that is often neglected by the existing maintenance theory is the weather condition. This paper proposes a new strategy that takes into account the electricity price and weather conditions, improves the expected profit of the systems, and reduce the overall maintenance and logistic costs. The maintenance schedule is formalized as an optimization problem where the discounted cumulative profit of a wind generation portfolio in a fixed-time horizon (e.g. two years ahead), subject to the technologically-derived maintenance time constraints is optimized. Both the theoretical and computational aspects of the proposed O&M strategy are discussed. Results show that taking into account market and weather opportunities in the design of the maintenance strategy, it is possible to achieve a more complete scheduling for a given set of wind power plants.

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